London (AFP) - Manchester City won their sixth Premier League match on the spin to underline their status as firm favourites but Liverpool clung on to their coat-tails after a dramatic late win against Everton.

Elsewhere on a Premier League weekend dominated by derbies, Arsenal beat Tottenham 4-2 and Chelsea overcame Claudio Ranieri’s Fulham 2-0.

The top five are now eight points clear of the chasing pack, with Manchester United, in seventh, looking increasingly unlikely to join the party after being held to a 2-2 draw by lowly Southampton.

Here are five things we learned from the Premier League this weekend:

- Liverpool show champion grit -

Winning ugly is a tired cliche but Liverpool are showing the mindset of champions as they refuse to let Premier League pacesetters Manchester City out of their sight.

Liverpool celebrate their late win against Everton at Anfield

Jurgen Klopp’s side are not playing with the same free-flowing verve as they did last season but just look at the numbers.

Liverpool pulled back to within two points of City with a 1-0 win against Everton after Divock Origi was in the right place to punish an astonishing error from England goalkeeper Jordan Pickford.

Liverpool have scored 16 goals fewer than City but have the meanest defence in the league – with just five goals conceded in 14 matches.

- All Guns blazing -

After the toxic atmosphere that characterised Arsenal home matches in the miserable final years of Arsene Wenger’s reign, it was hard to imagine the Emirates Stadium ever again becoming a raucous cauldron of emotion.

Pierre-Emerick Aubameyang scored twice as Arsenal beat Tottenham 4-2

Gunners fans had become used to their team choking on the big occasion but in just a few short months Unai Emery has got the fans of the north London club back on their feet.

A pulsating 4-2 win over arch-rivals Tottenham, which saw the Gunners recover from 2-1 down thanks to a second-half blitz, was a major statement of intent from Arsenal.

- City tough it out -

Bournemouth must hate the sight of Raheem Sterling after the England forward put champions Manchester City back into the lead with his eighth goal in six Premier League matches against the Cherries.

Raheem Sterling celebrates his goal against Bournemouth

Ilkay Gundogan added a third for a 3-1 victory in what looks on paper like a comfortable eighth successive home Premier League win this season but that hid the truth of a hard-earned win.

Bournemouth made it an uncomfortable afternoon for City and Pep Guardiola was delighted his team were able to dig deep.

“A good win, after the Champions League it is always tough,” said Guardiola. “People think it’s easy for us but that is not the truth so I like to win in this way.”

- Rashford offers hope for Mourinho -

Frustrated by Manchester United’s lack of killer instinct during their three-match winless run in the league, Jose Mourinho can take consolation from Marcus Rashford’s encouraging display in Saturday’s 2-2 draw against Southampton.

Manchester United forward Marcus Rashford set up both of his side's goals in the 2-2 draw at Southampton

Trailing 2-0 after a dismal opening at St Mary’s, United escaped an embarrassing defeat against Mark Hughes’s struggling side thanks to large part to Rashford’s contributions.

The 21-year-old has scored only twice for his club this season but he showed his value to United lies in more than his goal tally as the England forward provided assists for Romelu Lukaku and Ander Herrera as Mourinho’s men drew level before half-time.

“I have to say that I’m super happy with Marcus Rashford’s performance and he didn’t score a goal. So sometimes goals are not everything,” Mourinho said.

- Kante earns good report -

N’Golo Kante came in for some unexpected criticism from Maurizio Sarri after Chelsea were beaten 3-1 by Tottenham last week but he is back in his manager’s good books.

Chelsea midfielder N'Golo Kante in action against Fulham

The French World Cup winner set up Pedro’s opening goal in a 2-0 win against Fulham by winning the ball back in midfield.

“I think he played very well,” said Sarri. “He defended very well. He needs to improve a little more tactically but that’s natural.

“For the national team he usually plays with two midfielders. Last season sometimes with a two and sometimes with three, but in a central position, so it’s normal that he needs to improve.”